This activity involves rounding four-digit numbers to the nearest thousand.
What happens when you round these three-digit numbers to the nearest 100?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
What happens when you round these numbers to the nearest whole number?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
In this problem we are looking at sets of parallel sticks that
cross each other. What is the least number of crossings you can
make? And the greatest?
Find the sum of all three-digit numbers each of whose digits is
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the
numbers on each circle add up to the same amount. Can you find the
rule for giving another set of six numbers?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
Try adding together the dates of all the days in one week. Now
multiply the first date by 7 and add 21. Can you explain what
The number of plants in Mr McGregor's magic potting shed increases
overnight. He'd like to put the same number of plants in each of
his gardens, planting one garden each day. How can he do it?
Delight your friends with this cunning trick! Can you explain how
One block is needed to make an up-and-down staircase, with one step up and one step down. How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.
Choose any 3 digits and make a 6 digit number by repeating the 3
digits in the same order (e.g. 594594). Explain why whatever digits
you choose the number will always be divisible by 7, 11 and 13.
Can you explain how this card trick works?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
This challenge asks you to imagine a snake coiling on itself.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Can you dissect an equilateral triangle into 6 smaller ones? What
number of smaller equilateral triangles is it NOT possible to
dissect a larger equilateral triangle into?
Nim-7 game for an adult and child. Who will be the one to take the last counter?
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.
An investigation that gives you the opportunity to make and justify
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
We can arrange dots in a similar way to the 5 on a dice and they
usually sit quite well into a rectangular shape. How many
altogether in this 3 by 5? What happens for other sizes?
Find out what a "fault-free" rectangle is and try to make some of
How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?
Imagine starting with one yellow cube and covering it all over with
a single layer of red cubes, and then covering that cube with a
layer of blue cubes. How many red and blue cubes would you need?
What happens if you join every second point on this circle? How
about every third point? Try with different steps and see if you
can predict what will happen.
In how many different ways can you break up a stick of 7 interlocking cubes? Now try with a stick of 8 cubes and a stick of 6 cubes.
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable.
Decide which of these diagrams are traversable.
Consider all two digit numbers (10, 11, . . . ,99). In writing down
all these numbers, which digits occur least often, and which occur
most often ? What about three digit numbers, four digit numbers. . . .
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
Find some examples of pairs of numbers such that their sum is a
factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and
16 is a factor of 48.
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
While we were sorting some papers we found 3 strange sheets which
seemed to come from small books but there were page numbers at the
foot of each page. Did the pages come from the same book?
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.